
Now we use the identity (see, for example, [1]}),
\( \int _{S^{d-2}}e^{- i \mathbf {k}r \mathbf {n}} \mathrm {d}\mathbf {n}=\left(2\pi \right)^{\frac{d-1}{2}} \left|\mathbf {k}\right|^{\frac{3-d}{2}} r^{\frac{3-d}{2}}J_{\frac{d-3}{2}} \left( \left|\mathbf {k}\right|r \right)\quad \text{ for all }\left(\mathbf {k}, r\right) \in \mathbb {R}^{d-1} \times \left(0, \infty \right)\,.\) 
